Another mean of transportation that Rayong people like to use are motorcycles, they are very convenient and motorcycle taxi terminals can be found almost everywhere around the city. There are for example three of them just around Laemtong shopping mall, about 10 on Rajbamrung road (also called “sai-laang”) alone and ten as well around the bus terminal. So you won’t have problems finding one if you need one, and if you do not want to walk, try to get the number of one station or one motorbike driver, they can pick you up if they are not too far from you (though you would need to speak Thai for that).
As for the prices, motorbikes are more expensive than song-taews, it usually starts at fifteen baht for a short course, and can go up depending on your destination. For example, if you go from Laemtong to the mini-van terminal station (where you can pick-up van to go to Bangkok, Pattaya or other cities) it should cost you around 50 baht. But I think it is still reasonable and it is much more convenient, as you don’t have to wait for anybody and they can drop you off exactly where you want to. The main drawback is the same as it is usually with motorbikes in Thailand it may be dangerous.
Motorcycles stations operate from early morning until midnight approximately, but you will see that at night there are most likely fewer drivers.